Get a backup iso and try burning that to a dvd-r. I've had a few discs that wouldn't work despite very little scratching, in a funny way it's the rubbish DVD drive in the Wii that forced me into modding in the first place, when my Daughter's ever so slightly scratched Endless Ocean disc wouldn't play.

You need to configure the WiiKey to allow the update...

I have experianced a similar confusing issue with a different game from the same era as WiiFit. The behavior you are suffering from is the WiiKey preventing an update necessary for the game to load and run. You need to run the WiiKey configuration disc to instruct the WiiKey to allow the update to occur. (The official comparison chart does not show the original WiiKey as blocking updates, perhaps because it is not in all WiiKey firmware revisions.)

If you don't have firmware 1.9 for your region and a configuration disc you should be able to download the files required to make an update and configuration disc from Wiikey 2 Announced! Welcome to the official website of Wiikey! ... you will also need an actual GameCube controller, not the classic controller attachment for the WiiMote, because these are loaded as a GameCube disc.

After updating the WiiKey firmware to version 1.9 and then configuring the WiiKey to allow the system update and to not over-ride region coding (and restarting if necessary) - and after making sure the disc is for the same region as your Wii since the WiiKey would let a "wrong" region disc run and cause havoc if you ignored the preceeding or frustrate you if you didn't - insert the Wii game disc and it will update your system before the game loads and the game will play. There may not be any update prompts, but the game will play.

Now that the game plays, you might be wise to use the WiiKey configuration disc again to turn off system updates and override region coding again if you need that. This makes sure that you are in control of when a system update is installed in case your WiiKey would need to be updated before the system update to ensure continued operation. It also prevents problems that arise when playing discs that were created for a different region than your Wii that contain system updates - at best surplus shopping channels, but at worst a very confused Wii sometimes described as semi-bricked.